Questions: Inductive Strength: When Does Evidence Suffice?

Question 1

A pollster surveys 2,000 people at a single large political rally and concludes that 78% of voters support a particular policy. How should this argument be evaluated?

• A. Strong — the sample size of 2,000 is very large and exceeds most survey standards
• B. Weak — the sample is large but drawn from a deeply unrepresentative source, so the conclusion is not well-supported
• C. Strong — the conclusion is specific enough (78%) to be testable and falsifiable
• D. Weak — inductive arguments about political opinions can never be strong

Answer: (B)

Sample size alone does not determine inductive strength. A rally audience is self-selected and shares strong political views, making it unrepresentative of the general voting population. A large sample from a biased source remains a biased sample — it gives you a precise estimate of rally attendees' views, not voters generally. The argument is weak because the sample fails the representativeness criterion, despite its size. Option C confuses specificity of the stated conclusion with the quality of the evidence supporting it.

Question 2

Two arguments both draw on equally representative samples. Argument A concludes 'most surveyed adults prefer tea to coffee' and Argument B concludes 'all humans prefer tea to coffee.' Which is stronger, and why?

• A. Argument B is stronger because a universal claim is more scientifically significant
• B. Argument A is stronger because a more modest conclusion requires less evidence to support, so the same evidence provides stronger support for it
• C. They are equally strong because they use the same sample
• D. Argument B is stronger because falsifiable claims are always preferred in science

Answer: (B)

Inductive strength depends not just on the evidence but on the relationship between the evidence and the conclusion's scope. The more sweeping the conclusion, the more it goes beyond the evidence, and the weaker the argument. 'Most surveyed adults prefer tea' barely exceeds the evidence at all — it is almost directly observed. 'All humans prefer tea' extends to billions of unsurveyed people, past, present, and future. The same evidence supports the modest claim far more strongly than the universal one.

Question 3

A strong inductive argument can have true premises and still have a false conclusion.

• T. True
• F. False

Answer: True

This is the defining feature of inductive reasoning that separates it from deductive reasoning. Even an excellent inductive argument — large sample, highly representative, modest conclusion — only makes the conclusion probable, not certain. The classic example: observing millions of white swans across Europe over centuries strongly supports 'all swans are white.' The premises are all true. Yet the conclusion is false (black swans exist in Australia). Strength is about the degree of support, not a guarantee of truth.

Question 4

A larger sample generally makes an inductive argument stronger than a smaller sample.

• T. True
• F. False

Answer: False

Sample size is one of three key factors determining strength, and the others can override it. A large, biased sample can be weaker than a small, carefully representative one. Polling 10,000 people from a single demographic group tells you less about the general population than polling 200 people drawn systematically across all relevant subgroups. Representativeness — whether the sample reflects the diversity of the population — is often the more critical variable. Size amplifies whatever bias is already present rather than correcting it.

Question 5

How do sample size, representativeness, and conclusion specificity interact to determine inductive strength? Can you compensate for weakness in one factor by improving another?

Model answer: The three factors interact multiplicatively rather than independently. A small but highly representative sample can outperform a large biased one. A very specific (modest) conclusion requires less evidence and so can be strongly supported by a smaller or less comprehensive sample. You can compensate for limited sample size by increasing representativeness, and for a broad or sweeping conclusion you need both larger size and better representativeness. The key skill is identifying which factor is the weak link and assessing whether the overall balance of evidence justifies the conclusion's scope.

This interaction is what makes inductive evaluation a genuine skill rather than a checklist. 'I've talked to a lot of people' bundles together size and representativeness without distinguishing them. Asking 'how many, how selected, and how specific is the conclusion?' forces each factor into focus. Cognitive biases like availability bias and confirmation bias distort our intuitive assessments of all three — which is why explicit evaluation against these criteria is useful.